-4x(x-1)=2(x-4)

Solution for -4x(x-1)=2(x-4) equation:

-4x(x-1)=2(x-4)

We move all terms to the left:

-4x(x-1)-(2(x-4))=0

We multiply parentheses

-4x^2+4x-(2(x-4))=0


We calculate terms in parentheses: -(2(x-4)), so:

2(x-4)

We multiply parentheses

2x-8

Back to the equation:

-(2x-8)


We get rid of parentheses

-4x^2+4x-2x+8=0

We add all the numbers together, and all the variables

-4x^2+2x+8=0

a = -4; b = 2; c = +8;
Δ = b2-4ac
Δ = 22-4·(-4)·8
Δ = 132
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{33}}{2*-4}=\frac{-2-2\sqrt{33}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{33}}{2*-4}=\frac{-2+2\sqrt{33}}{-8}
$